Least squares estimation for the linear self-repelling diffusion driven by α-stable motions

Abstract In this paper, we consider parameter estimations of the linear self-repelling diffusion X t α = M t α − θ ∫ 0 t ∫ 0 s ( X s α − X r α ) d r d s + ν t , where θ 0 , ν ∈ R and M α is a symmetrical α -stable motion on R ( 1 α 2 ). The process is an analogue of the self-repelling diffusion (see Durrett and Rogers (1992) and Cranston and Le Jan (1995)). By using least squares method, we study estimators of θ and ν and give their asymptotic distributions under the discrete observation.